Results 41 to 50 of about 1,933 (161)
On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series [PDF]
, 2003 Using Krattenthaler's operator method, we give a new proof of Warnaar's recent elliptic extension of Krattenthaler's matrix inversion. Further, using a theta function identity closely related to Warnaar's inversion, we derive summation and transformation
Andrews +30 more
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Hyperbolic beta integrals [PDF]
, 2004 Hyperbolic beta integrals are analogues of Euler's beta integral in which the role of Euler's gamma function is taken over by Ruijsenaars' hyperbolic gamma function.
Stokman, Jasper V.
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Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions [PDF]
, 2009 We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this ...
Rains, Eric M., van de Bult, Fokko J.
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A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series
, 2000 In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system A_n. First, we apply Ismail's argument to an A_n q-binomial theorem of Milne and derive a new A_n generalization of Ramanujan's 1-psi-1 ...
Milne, S. C., Schlosser, M.
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A new multivariable 6-psi-6 summation formula [PDF]
, 2006 By multidimensional matrix inversion, combined with an A_r extension of Jackson's 8-phi-7 summation formula by Milne, a new multivariable 8-phi-7 summation is derived.
C. Krattenthaler +31 more
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On transformation of certain bilateral basic hypergeometric series and their applications
Proceedings - Mathematical Sciences, 2019 In this paper, we obtain new transformation and summation formulae for bilateral basic hypergeometric series and give a simple proof of Jacobi’s triple product identity. Further, we present applications of the main results.
K N Vidya, D D Somashekara
openaire +2 more sources
A simple proof of Bailey's very-well-poised 6-psi-6 summation
, 2000 We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauss' 2-F-1 summation and elementary series manipulations to give a simple proof of Dougall's 2-H-2 summation ...
Schlosser, M.
core +1 more source
Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations [PDF]
, 2003 Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10-phi-9 transformation. From this result, we deduce new multivariable terminating 10-phi-9 transformations, 8-phi-7 summations ...
Andrews +24 more
core +4 more sources
Multilateral inversion of A_r, C_r and D_r basic hypergeometric series
, 2006 In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series.
D.M. Bressoud +22 more
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Developmental Medicine &Child Neurology, EarlyView.Several functional connections between ROIs in the somatomotor (purple) and the default mode network (gray) were significantly associated with the MABC‐2 “aiming and catching” sub‐domain in the HIE cohort in comparison to controls. The colors of the connections represents the correlation coefficient with either negative (light blue to magenta) or ...
Gustaf Håkansson +5 more
wiley +1 more source